On the intersection of maximal partial clones and the join of minimal partial clones

Let A be a nonsingleton finite set and M be a family of maximal partial clones with trivial intersection over A. What is the smallest possible cardinality of M? Dually, if F is a family of minimal partial clones whose join is the set of all partial functions on A, then what is the smallest possible cardinality of F? The purpose of this note is to present results related to these two problems.

[1]  B. Csákány.  All minimal clones on the three-element set , 1983, Acta Cybern..

[2]  Lucien Haddad,et al.  Completeness theory for finite partial algebras , 1992 .

[3]  László Szabó.  On Minimal and Maximal Clones II , 1998, Acta Cybern..

[4]  I. Rosenberg.  MINIMAL CLONES I: THE FIVE TYPES , 1986 .

[5]  Reinhard Pöschel,et al.  Minimal partial clones , 1991, Bulletin of the Australian Mathematical Society.

[6]  Péter P. Pálfy,et al.  On Binary Minimal Clones , 1996, Acta Cybern..

[7]  Lucien Haddad,et al.  Maximal partial clones determined by the areflexive relations , 1989, Discret. Appl. Math..

[8]  Lucien Haddad,et al.  Partial clones and their generating sets , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).

[9]  Ivo G. Rosenberg,et al.  Gigantic pairs of minimal clones , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).